Sunday

February 1, 2015

February 1, 2015

Posted by **thomas** on Tuesday, October 13, 2009 at 5:06pm.

lim arctan[(x^2 - 4)/(3x^2-6x)]

x->2

- calculus -
**Reiny**, Tuesday, October 13, 2009 at 5:26pmMy first step in doing limits is to sub in the approach value, this will give me Lim arctan (0/0)

This just about guarantees that the algebraic expression will factor and the offending factor will cancel.

Sure enough

lim arctan[(x^2 - 4)/(3x^2-6x)] x->2

= lim arctan[(x+2)(x-2)]/[3x(x-2)]

=lim arctan[(x+2)]/[3x]

= lim arctan(2/3)

now use your calculator, set to radian mode, to find

lim arctan[(x^2 - 4)/(3x^2-6x)] x->2

= .588

- calculus -
**thomas**, Tuesday, October 13, 2009 at 5:30pmthanks for the reply... the question asks me to evaluate the limit using continuity, how do i justify my answer with continuity?

**Answer this Question**

**Related Questions**

Calculus - Note that pi lim arctan(x ) = ---- x -> +oo 2 Now evaluate / pi \ ...

Calculus - I am maybe overthinking this, but what is the lim as n-> infinity ...

limiting position of the particle - A particle moves along the x axis so that ...

Calculus - Find the limit. lim 5-x/(x^2-25) x-->5 Here is the work I have so ...

Calculus. Limits. Check my answers, please! :) - 4. lim (tanx)= x->pi/3 -(...

calculus again - Suppose lim x->0 {g(x)-g(0)} / x = 1. It follows necesarily ...

Calculus (lim) - consider the statement lim x³-6x²+11x-6 / x-1 = 2 x->1 Using...

Calculus - Show that limit as n approaches infinity of (1+x/n)^n=e^x for any x&...

Calculus - Show that limit as n approaches infinity of (1+x/n)^n=e^x for any x&...

calculus - lim (x^3-1)/(x^3+2x^2y+xy^2-x^2-2xy-y^2) (x,y)->(1,0) my question ...